Circular reasoning warning: because that’s how species are defined (i.e. two individuals belong to different species if they cannot produce viable, fertile offspring). Now, this definition breaks down in some cases but it’s still the common definition.
–
Konrad RudolphMay 23 '12 at 9:28

As an exception to this rule, you may want to read about the amazon molly or the fire ants. You'll find more info about these species and references in this answer
–
Remi.bMay 6 at 4:14

The biological environment in every cell and tissue of your body is an extremely complex, tightly controlled system. There are tens of thousands of genes in a typical eukaryotic genome, and depending on tissue types and environmental conditions, these genes are turned on and off in a very controlled manner. There is regulation at every point in the flow of genetic information: nucleosome disruption to expose DNA; RNA transcription from the DNA; protein translation from the RNA; and in some cases, additional modifications of proteins or intermediate mRNAs. At early stages in development, regulation of RNA and protein levels is even more crucial than, say, when an organism is fully developed and healthy.

All living organisms share some basic building blocks--DNA, RNA, and proteins work pretty much the same in all of life (there are a few rare variations of the genetic code but the basic premise is identical). However, the way that specific genes, transcripts, and proteins work together to sustain life varies widely between different organisms.

For a very rough analogy, imagine you want to bake a batch of cookies. Then consider the three following scenarios.

You look at two different recipes for chocolate chip cookies. They will have some slight differences, but they will share a lot in common. If you put the ingredients for both recipes in one bowl, it's likely you can still come up with some pretty good chocolate chip cookies in the end.

You look at two different recipes: one for chocolate chip cookies, and one for chocolate muffins. There will be some big differences in these recipes, but combining all the ingredients and baking, you still might be able to come up with something edible (and maybe even tasty).

You look at two different recipes: one for chocolate chip cookies, and one for French onion soup. If you combine the ingredients from these recipes and try to cook or bake them, there is no way you will come up with something that anyone would want to eat.

The first example we can relate to two individuals of the same species mating. Of course there is natural variation in the population, but this doesn't typically lead to lethality during development. The second example we can relate to individuals of two related species (such as a horse and a donkey). Sometimes these matings can produce viable offspring, although these offspring are often sterile. The third example we can relate to individuals of two very divergent species (such as donkey and dog in your original question). The biological systems inside donkeys are just so different from those inside dogs that this mating cannot produce a viable offspring.

Admittedly this is a rough analogy, but hopefully is sheds some light on the issue.

Often, they do fuse together but the chromosome pairing is not precise enough to guarantee faithful cell division without loss of genetic material. Consider for example a simple inversion of one large part of a chromosome. In a closely related species that does not have this inversion, either the inverted part pairs or the non-inverted ends pair, but never the whole chromosome. That leads to strand-breaks and loss of large amounts of genetic material. That's an easy event for speciation, since it does not disrupt much. Only the ends where the inverted piece joins has two disruption. So, maximally two genes might be broken, but the chromosomes modified in this way won't pair.